scholarly journals A note on L2-boundary integrals of the Bergman kernel

2018 ◽  
Vol 29 (14) ◽  
pp. 1871001 ◽  
Author(s):  
Phung Trong Thuc
Keyword(s):  
Bergman Kernel ◽  
Pseudoconvex Domains ◽  
Boundary Integrals

In this paper, we obtain some estimates on the [Formula: see text]-boundary norm of the Bergman kernel for pseudoconvex domains admitting a plurisubharmonic defining function.

The Bergman kernel on uniformly extendable pseudoconvex domains

1986 ◽  
Vol 273 (3) ◽  
pp. 471-478 ◽  
Author(s):  
Klas Diederich ◽  
Gregor Herbort ◽  
Takeo Ohsawa
Keyword(s):  
Bergman Kernel ◽  
Pseudoconvex Domains

scholarly journals On some extremal problems in Bergman spaces in weakly pseudoconvex domains

2018 ◽  
Vol 26 (2) ◽  
pp. 83-97
Author(s):  
Romi F. Shamoyan ◽  
Olivera R. Mihić
Keyword(s):  
Distance Function ◽  
Bergman Kernel ◽  
Additional Condition ◽  
Bergman Spaces ◽  
Representation Formula ◽  
Extremal Problems ◽  
Bergman Projection ◽  
Pseudoconvex Domains ◽  
Weakly Pseudoconvex

AbstractWe consider and solve extremal problems in various bounded weakly pseudoconvex domains in ℂn based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces $A_\alpha ^p$ in such type domains. We provide some new sharp theorems for distance function in Bergman spaces in bounded weakly pseudoconvex domains with natural additional condition on Bergman representation formula.

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